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Relational Blockworld: A Path Integral Based Interpretation of Quantum Field Theory

Michael , Silberstein (2011) Relational Blockworld: A Path Integral Based Interpretation of Quantum Field Theory. In: [2010] Philosophy of Science Assoc. 22nd Biennial Mtg (Montréal, QC) > PSA 2010 Contributed Papers.

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    Abstract

    We propose a new path integral based interpretation of quantum field theory (QFT). In
    our interpretation, QFT is the continuous approximation of a more fundamental, discrete
    graph theory (theory X) whereby the transition amplitude Z is not viewed as a sum over
    all paths in configuration space, but measures the symmetry of the differential operator
    and source vector of the discrete graphical action. We propose that the differential
    operator and source vector of theory X are related via a self-consistency criterion (SCC)
    based on the identity that underwrites divergence-free sources in classical field theory,
    i.e., the boundary of a boundary principle. In this approach, the SCC ensures the source
    vector is divergence-free and resides in the row space of the differential operator.
    Accordingly, the differential operator will necessarily have a non-trivial eigenvector with
    eigenvalue zero, so the SCC is the origin of gauge invariance. Factors of infinity
    associated with gauge groups of infinite volume are excluded in our approach, since Z is
    restricted to the row space of the differential operator and source vector. We show it is
    possible that the underlying theory X, despite being discrete, is the basis for exact
    Poincaré invariance. Using this formalism, we obtain the two-source transition amplitude
    over a (1+1)-dimensional graph with N vertices fundamental to the scalar Gaussian
    theory and interpret it in the context of the twin-slit experiment to provide a unified
    account of the Aharonov-Bohm effect and quantum non-separability (superposition and
    entanglement) that illustrates our ontic structural realist alternative to problematic particle
    and field ontologies. Our account also explains the need for regularization and
    renormalization, explains gauge invariance and largely discharges the problems of
    inequivalent representations and Haag’s theorem. This view suggests corrections to
    general relativity via modifications to its graphical counterpart, Regge calculus. We
    conclude by presenting the results of our modified Regge calculus approach to Einsteinde
    Sitter cosmology where we produced a fit to the Union2 Compilation data for type Ia
    supernovae rivaling that of the concordance model (ΛCDM), but without having to
    invoke dark energy or accelerated expansion.


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    Item Type: Conference or Workshop Item (UNSPECIFIED)
    Keywords: quantum field theory, path integral, renormalization
    Subjects: Specific Sciences > Physics
    Specific Sciences > Physics > Quantum Field Theory
    Conferences and Volumes: [2010] Philosophy of Science Assoc. 22nd Biennial Mtg (Montréal, QC) > PSA 2010 Contributed Papers
    Depositing User: Michael Silberstein
    Date Deposited: 20 Oct 2011 07:31
    Last Modified: 20 Oct 2011 07:31
    Item ID: 8851
    URI: http://philsci-archive.pitt.edu/id/eprint/8851

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